24.0 JMtjcellanea Curio fa* 



aa-\-iax~\r xx — J% whence y = \/ xax-\-xx* 



Confequently HL = a-\ -x~\- \fiax-\-xxj and 



PG == a x — \l xax-\-xx. Wherefore the 

 Fluxion of HL, or /w, is 



— 5 - ■■ ■ — . And became or the 



V iax\xx 

 limilar Triangles ImL, LHS, 'tis LH : HS 

 Im : mL whence mL or df the Fluxion of 



BD, is ±= — That is, the Curve 



AD, generated after the foregoing manner, 

 from the Logarithmical Curve, is of fuch a 

 Nature, that if the Axis be x y and its 



Fluxion at, the Fluxion of the Ordinate BD 



ax 



is «. But this is the Property of 



\J 2.ax-\-xx 



the Catenaria corresponding to the right Line 

 a i as was demonstrated at Prof. I. There- 

 fore the Curve FAD defer ib'd as above, is 

 this very Cat en aria it felf. Q/ E : D. 



C O- 



